Door sweeps having flexible sealing members for mounting on a door are known. When the door sweep is mounted on a door that is suspended within a door frame defining a door opening, the flexible sealing member serves to provide a sealing function or sealing effect between the bottom end of the door and the corresponding bottom surface of the door opening when the door assumes its closed position. With the repeated opening and closing of the door, the flexible sealing member sweeps across the bottom surface of the door opening and, overtime, the flexible sealing member can wear-down, break, tear, etc. which damage can adversely affect the quality of sealing function provided by the door sweep and can entirely defeat the sealing function or sealing effect previously provided by the door. Accordingly, door sweeps that offer improved longevity which can help to ensure that an adequate sealing function or sealing effect is provided between the door and the corresponding bottom surface of a door opening are desirable.